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1 of 8 0-day streak

Use z-score boundaries to estimate normal-model percentages and counts

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
Given z-scores: lower-tail percentageGiven z-scores: upper-tail percentageGiven z-scores: interval percentageGiven observations: lower-tail percentageGiven observations: upper-tail percentageGiven observations: interval percentageNOWMix of allRecommended
Question 1 of 8

Calculator allowed

For daily water use in a household, in litres, the mean is 44 L and the standard deviation is 6 L. Assume the distribution is approximately symmetric and bell-shaped

The ordered boundary values are 26 L and 62 L

Use a normal model and the 68–95–99.7% empirical rule. Use these percentages without intermediate rounding; report the resulting estimate, not a calculator normal-CDF value

(a)2 marks

Complete the signed z-score for each actual boundary

(b)1 mark

Using the empirical rule, what percentage of values are between the two boundary values?

Use a normal model and the 68–95–99.7% empirical rule. Use these percentages without intermediate rounding; report the resulting estimate, not a calculator normal-CDF value

Format: empirical-rule percentage estimate